Nonparametric Involutive Markov Chain Monte Carlo

Carol Mak, Fabian Zaiser, Luke Ong
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:14802-14859, 2022.

Abstract

A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo (NP-iMCMC) algorithm as a method for constructing MCMC inference algorithms for nonparametric models expressible in universal PPLs. Building on the unifying involutive MCMC framework, and by providing a general procedure for driving state movement between dimensions, we show that NP-iMCMC can generalise numerous existing iMCMC algorithms to work on nonparametric models. We prove the correctness of the NP-iMCMC sampler. Our empirical study shows that the existing strengths of several iMCMC algorithms carry over to their nonparametric extensions. Applying our method to the recently proposed Nonparametric HMC, an instance of (Multiple Step) NP-iMCMC, we have constructed several nonparametric extensions (all of which new) that exhibit significant performance improvements.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-mak22a, title = {Nonparametric Involutive {M}arkov Chain {M}onte {C}arlo}, author = {Mak, Carol and Zaiser, Fabian and Ong, Luke}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {14802--14859}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/mak22a/mak22a.pdf}, url = {https://proceedings.mlr.press/v162/mak22a.html}, abstract = {A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo (NP-iMCMC) algorithm as a method for constructing MCMC inference algorithms for nonparametric models expressible in universal PPLs. Building on the unifying involutive MCMC framework, and by providing a general procedure for driving state movement between dimensions, we show that NP-iMCMC can generalise numerous existing iMCMC algorithms to work on nonparametric models. We prove the correctness of the NP-iMCMC sampler. Our empirical study shows that the existing strengths of several iMCMC algorithms carry over to their nonparametric extensions. Applying our method to the recently proposed Nonparametric HMC, an instance of (Multiple Step) NP-iMCMC, we have constructed several nonparametric extensions (all of which new) that exhibit significant performance improvements.} }
Endnote
%0 Conference Paper %T Nonparametric Involutive Markov Chain Monte Carlo %A Carol Mak %A Fabian Zaiser %A Luke Ong %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-mak22a %I PMLR %P 14802--14859 %U https://proceedings.mlr.press/v162/mak22a.html %V 162 %X A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo (NP-iMCMC) algorithm as a method for constructing MCMC inference algorithms for nonparametric models expressible in universal PPLs. Building on the unifying involutive MCMC framework, and by providing a general procedure for driving state movement between dimensions, we show that NP-iMCMC can generalise numerous existing iMCMC algorithms to work on nonparametric models. We prove the correctness of the NP-iMCMC sampler. Our empirical study shows that the existing strengths of several iMCMC algorithms carry over to their nonparametric extensions. Applying our method to the recently proposed Nonparametric HMC, an instance of (Multiple Step) NP-iMCMC, we have constructed several nonparametric extensions (all of which new) that exhibit significant performance improvements.
APA
Mak, C., Zaiser, F. & Ong, L.. (2022). Nonparametric Involutive Markov Chain Monte Carlo. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:14802-14859 Available from https://proceedings.mlr.press/v162/mak22a.html.

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